Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule

Christian Ringhofer, M. Nedjalkov, H. Kosinas, S. Selberherr

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We derive a quantum mechanical correction to the semiclassical Fermi golden rule operator for scattering of electrons in a crystal. This correction takes into account the fact that electron-phonon interaction is not instantaneous in quantum mechanics. The corrective term is derived via an oscillatory, i.e., weak, limit in the Levinson equation for large timescales.

Original languageEnglish (US)
Pages (from-to)1933-1953
Number of pages21
JournalSIAM Journal on Applied Mathematics
Volume64
Issue number6
DOIs
StatePublished - 2004

Fingerprint

Fermi's Golden Rule
Electron-phonon Interaction
Semiclassical Approximation
Electron-phonon interactions
Phonon scattering
Weak Limit
Electron scattering
Quantum theory
Phonon
Quantum Mechanics
Instantaneous
Time Scales
Crystal
Scattering
Electron
Crystals
Electrons
Term
Operator

Keywords

  • Asymptotic analysis
  • Boltzmann equation
  • Fermi's golden rule
  • Levinson equation
  • Quantum mechanics
  • Wigner functions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule. / Ringhofer, Christian; Nedjalkov, M.; Kosinas, H.; Selberherr, S.

In: SIAM Journal on Applied Mathematics, Vol. 64, No. 6, 2004, p. 1933-1953.

Research output: Contribution to journalArticle

Ringhofer, Christian ; Nedjalkov, M. ; Kosinas, H. ; Selberherr, S. / Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule. In: SIAM Journal on Applied Mathematics. 2004 ; Vol. 64, No. 6. pp. 1933-1953.
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